Francesco Maggi - OMT




Ars Inveniendi

Sets of Finite Perimeter &
Geometric Variational Problems

Optimal Mass Transport on Euclidean Spaces

Optimal Mass Transport
on Euclidean Spaces



You are still doing things that I gave up years ago
-- Lou Reed

And if the homework brings you down
then we'll throw it on the fire and take the car downtown
-- David Bowie

Remarks, misprints and errata (nothing here... yet!)


"Francesco Maggi's book is a detailed and extremely well written explanation
of the fascinating theory of Monge-Kantorovich optimal mass transfer.
I especially recommend Part IV's discussion of the ‘linear’ cost problem
and its subtle mathematical resolution."

Lawrence C. Evans, University of California, Berkeley

"Over the last three decades, optimal transport has revolutionized
the mathematical analysis of inequalities, differential equations, dynamical systems,
and their applications to physics, economics, and computer science. By exposing the interplay
between the discrete and Euclidean settings, Maggi's book makes this development uniquely
accessible to advanced undergraduates and mathematical researchers with a minimum of prerequisites.
It includes the first textbook accounts of the localization technique known as needle decomposition
and its solution to Monge's centuries old cutting and filling problem (1781).
This book will be an indispensable tool for advanced undergraduates
and mathematical researchers alike."

Robert McCann, University of Toronto